Increased burst size in multiply infected cells can alter basic virus dynamics

A nomogram to predict anal condyloma acuminatum recurrence in HIV-negative patients following photodynamic therapy: A decade-long retrospective clinical study at a single tertiary hospital

BACKGROUND

Anal condyloma acuminatum (CA) is marked by its thorny treatment and high recurrence rate. Although 5-aminolevulinic acid photodynamic therapy (ALA-PDT) demonstrates significant efficacy and safety in treating anal CA, it does not completely prevent recurrence. This study aimed to develop and validate a nomogram model in predicting the risk of relapse in HIV-negative patients with anal CA following treatment with ALA-PDT.

METHODS

A retrospective analysis was conducted on patients diagnosed with anal CA who received combined CO2 laser vaporization and ALA-PDT between January 2013 and May 2023. Patients were divided into recurrence and non-recurrence groups. A nomogram was developed based on factors showing statistical significance in multivariable logistic regression analysis. The discriminative ability and clinical utility of the nomogram were assessed via ROC curves and decision curve analysis, with internal validation performed through bootstrap resampling.

RESULTS

Among the 176 patients included, 33 (18.75 %) experienced recurrence, while 143 did not. Independent predictors for recurrence included HPV types, history of anal intercourse, and the number of CO2 laser treatments received. Incorporating these predictors, the nomogram demonstrated a superior diagnostic performance (area under the curve = 0.881, 95 % CI: 0.818-0.935) and a significant net benefit in decision curve analysis.

CONCLUSIONS

The nomogram accurately predicts the risk of recurrence in HIV-negative patients with anal CA following ALA-PDT. It offers a valuable tool for guiding preoperative clinical decision-making and establishing personalized treatment strategies to minimize the risk of relapse.

Modeling dynamics of acute HIV infection incorporating density-dependent cell death and multiplicity of infection

Understanding the dynamics of acute HIV infection can offer valuable insights into the early stages of viral behavior, potentially helping uncover various aspects of HIV pathogenesis. The standard viral dynamics model explains HIV viral dynamics during acute infection reasonably well. However, the model makes simplifying assumptions, neglecting some aspects of HIV infection. For instance, in the standard model, target cells are infected by a single HIV virion. Yet, cellular multiplicity of infection (MOI) may have considerable effects in pathogenesis and viral evolution. Further, when using the standard model, we take constant infected cell death rates, simplifying the dynamic immune responses. Here, we use four models-1) the standard viral dynamics model, 2) an alternate model incorporating cellular MOI, 3) a model assuming density-dependent death rate of infected cells and 4) a model combining (2) and (3)-to investigate acute infection dynamics in 43 people living with HIV very early after HIV exposure. We find that all models qualitatively describe the data, but none of the tested models is by itself the best to capture different kinds of heterogeneity. Instead, different models describe differing features of the dynamics more accurately. For example, while the standard viral dynamics model may be the most parsimonious across study participants by the corrected Akaike Information Criterion (AICc), we find that viral peaks are better explained by a model allowing for cellular MOI, using a linear regression analysis as analyzed by R2. These results suggest that heterogeneity in within-host viral dynamics cannot be captured by a single model. Depending on the specific aspect of interest, a corresponding model should be employed.

A mathematical model for HIV dynamics with multiple infections: implications for immune escape

Multiple infections enable the recombination of different strains, which may contribute to viral diversity. How multiple infections affect the competition dynamics between the two types of strains, the wild and the immune escape mutant, remains poorly understood. This study develops a novel mathematical model that includes the two strains, two modes of viral infection, and multiple infections. For the representative double-infection case, the reproductive numbers are derived and global stabilities of equilibria are obtained via the Lyapunov direct method and theory of limiting systems. Numerical simulations indicate similar viral dynamics regardless of multiplicities of infections though the competition between the two strains would be the fiercest in the case of quadruple infections. Through sensitivity analysis, we evaluate the effect of parameters on the set-point viral loads in the presence and absence of multiple infections. The model with multiple infections predict that there exists a threshold for cytotoxic T lymphocytes (CTLs) to minimize the overall viral load. Weak or strong CTLs immune response can result in high overall viral load. If the strength of CTLs maintains at an intermediate level, the fitness cost of the mutant is likely to have a significant impact on the evolutionary dynamics of mutant viruses. We further investigate how multiple infections alter the viral dynamics during the combination antiretroviral therapy (cART). The results show that viral loads may be underestimated during cART if multiple-infection is not taken into account.

A hybrid discrete-continuum model of immune responses to SARS-CoV-2 infection in the lung alveolar region, with a focus on interferon induced innate response

We develop a lattice-based, hybrid discrete-continuum modeling framework for SARS-CoV-2 exposure and infection in the human lung alveolar region, or parenchyma, the massive surface area for gas exchange. COVID-19 pneumonia is alveolar infection by the SARS-CoV-2 virus significant enough to compromise gas exchange. The modeling framework orchestrates the onset and progression of alveolar infection, spatially and temporally, beginning with a pre-immunity baseline, upon which we superimpose multiple mechanisms of immune protection conveyed by interferons and antibodies. The modeling framework is tunable to individual profiles, focusing here on degrees of innate immunity, and to the evolving infection-replication properties of SARS-CoV-2 variant strains. The model employs partial differential equations for virion, interferon, and antibody concentrations governed by diffusion in the thin fluid coating of alveolar cells, species and lattice interactions corresponding to sources and sinks for each species, and multiple immune protections signaled by interferons. The spatial domain is a two-dimensional, rectangular lattice of alveolar type I (non-infectable) and type II (infectable) cells with a stochastic, species-concentration-governed, switching dynamics of type II lattice sites from healthy to infected. Once infected, type II cells evolve through three phases: an eclipse phase during which RNA copies (virions) are assembled; a shedding phase during which virions and interferons are released; and then cell death. Model simulations yield the dynamic spread of, and immune protection against, alveolar infection and viral load from initial sites of exposure. We focus in this paper on model illustrations of the diversity of outcomes possible from alveolar infection, first absent of immune protection, and then with varying degrees of four known mechanisms of interferon-induced innate immune protection. We defer model illustrations of antibody protection to future studies. Results presented reinforce previous recognition that interferons produced solely by infected cells are insufficient to maintain a high efficacy level of immune protection, compelling additional mechanisms to clear alveolar infection, such as interferon production by immune cells and adaptive immunity (e.g., T cells). This manuscript was submitted as part of a theme issue on "Modelling COVID-19 and Preparedness for Future Pandemics".

The ratio versus difference optimization and its implications for optimality theory

Among the classical models of optimization, some models maximize the ratio of returns to investment and others maximize the difference between returns and investment. However, an understanding of under what conditions the ratio or the difference approaches are appropriate is still fragmentary. Under specific contexts, it has been stated that when the investable amount, but not the opportunity for investment, is perceived to be limiting, a ratio optimum is appropriate, whereas a difference optimum is appropriate when the opportunity for investment, but not the investable amount, is perceived to be limiting. The question is important because the strategies indicated by ratio optimum can be substantially different than the ones suggested by difference optimum. We make a general case here to examine and expand this principle and apply it to many evolutionary ecological problems including parental investment, offspring quality-quantity trade-off, nectar production, pollinator behavior viral burst size, and intracellular protein handling. We show that the ratio-difference distinction in optimization models resolves many long-standing debates and conundrums in evolution and behavior.

Viro-fluidics: Real-time analysis of virus production kinetics at the single-cell level

Real-time visualization and quantification of viruses released by a cell are crucial to further decipher infection processes. Kinetics studies at the single-cell level will circumvent the limitations of bulk assays with asynchronous virus replication. We have implemented a "viro-fluidic" method, which combines microfluidics and virology at single-cell and single-virus resolutions. As an experimental model, we used standard cell lines producing fluorescent HIV-like particles (VLPs). First, to scale the strategy to the single-cell level, we validated a sensitive flow virometry system to detect VLPs in low concentration samples (≥10⁴ VLPs/mL). Then, this system was coupled to a single-cell trapping device to monitor in real-time the VLPs released, one at a time, from single cells under cell culture conditions. Our results revealed an average production rate of 50 VLPs/h/cell similar to the rate estimated for the same cells grown in population. Thus, the virus-producing capacities of the trapped cells were preserved and its real-time monitoring was accurate. Moreover, single-cell analysis revealed a release of VLPs with stochastic bursts with typical time intervals of few minutes, revealing the existence of limiting step(s) in the virus biogenesis process. Our tools can be applied to other pathogens or to extracellular vesicles to elucidate the dissemination mechanisms of these biological nanoparticles.

Superinfection exclusion: A viral strategy with short-term benefits and long-term drawbacks

Viral superinfection occurs when multiple viral particles subsequently infect the same host. In nature, several viral species are found to have evolved diverse mechanisms to prevent superinfection (superinfection exclusion) but how this strategic choice impacts the fate of mutations in the viral population remains unclear. Using stochastic simulations, we find that genetic drift is suppressed when superinfection occurs, thus facilitating the fixation of beneficial mutations and the removal of deleterious ones. Interestingly, we also find that the competitive (dis)advantage associated with variations in life history parameters is not necessarily captured by the viral growth rate for either infection strategy. Putting these together, we then show that a mutant with superinfection exclusion will easily overtake a superinfecting population even if the latter has a much higher growth rate. Our findings suggest that while superinfection exclusion can negatively impact the long-term adaptation of a viral population, in the short-term it is ultimately a winning strategy.

Viral social behaviour has recently been receiving increasing attention in the context of ecological and evolutionary dynamics of viral populations. One fascinating and still relatively poorly understood example is superinfection or co-infection, which occur when multiple viruses infect the same host. Among bacteriophages, a wide range of mechanisms have been discovered that enable phage to prevent superinfection (superinfection exclusion) even at the cost of using precious resources for this purpose. What is the evolutionary impact of this strategic choice and why do so many phages exhibit this behaviour? Here, we conduct an extensive simulation study of a phage population to address this question. In particular, we investigate the fate of viral mutations arising in an environment with a constant supply of bacterial hosts designed to mimic a “turbidostat,” as these are increasingly being used in laboratory evolution experiments. Our results show that allowing superinfection in the long-term yields a population which is more capable of adapting to changes in the environment. However, when in direct competition, mutants capable of preventing superinfection experience a very large advantage over their superinfecting counterparts, even if this ability comes at a significant cost to their growth rate. This indicates that while preventing superinfection can negatively impact the long-term prospects of a viral population, in the short-term it is ultimately a winning strategy.

Modelling Degradation and Replication Kinetics of the Zika Virus In Vitro Infection

Mathematical models of in vitro viral kinetics help us understand and quantify the main determinants underlying the virus–host cell interactions. We aimed to provide a numerical characterization of the Zika virus (ZIKV) in vitro infection kinetics, an arthropod-borne emerging virus that has gained public recognition due to its association with microcephaly in newborns. The mathematical model of in vitro viral infection typically assumes that degradation of extracellular infectious virus proceeds in an exponential manner, that is, each viral particle has the same probability of losing infectivity at any given time. We incubated ZIKV stock in the cell culture media and sampled with high frequency for quantification over the course of 96 h. The data showed a delay in the virus degradation in the first 24 h followed by a decline, which could not be captured by the model with exponentially distributed decay time of infectious virus. Thus, we proposed a model, in which inactivation of infectious ZIKV is gamma distributed and fit the model to the temporal measurements of infectious virus remaining in the media. The model was able to reproduce the data well and yielded the decay time of infectious ZIKV to be 40 h. We studied the in vitro ZIKV infection kinetics by conducting cell infection at two distinct multiplicity of infection and measuring viral loads over time. We fit the mathematical model of in vitro viral infection with gamma distributed degradation time of infectious virus to the viral growth data and identified the timespans and rates involved within the ZIKV-host cell interplay. Our mathematical analysis combined with the data provides a well-described example of non-exponential viral decay dynamics and presents numerical characterization of in vitro infection with ZIKV.

Method for serial passage of infectious hematopoietic necrosis virus (IHNV) in rainbow trout

Transmission is a fundamental component of pathogen fitness. A better understanding of pathogen transmission can greatly improve disease management. In particular, controlled studies of multiple rounds of natural transmission (i.e. serial passage) can provide powerful epidemiological and evolutionary inferences. However, such studies are possible in only a few systems because of the challenges in successfully initiating and maintaining transmission in the laboratory. Here we developed an efficient and reproducible cohabitation method for conducting controlled experiments investigating the effects of serial passage on infectious hematopoietic necrosis virus (IHNV) in rainbow trout. This method was used to investigate the transmission efficiency and kinetics of viral shedding of IHNV over 3 serial passages. Transmission efficiency decreased from 100 to 62.5% over the passage steps and was associated with a decrease in virus shedding into water. A shift in the peak of viral shedding was also observed, from Day 2 post immersion for passage 0 to at least 24 h later for all subsequent passages. Finally, the characterization of viruses after 1 round of transmission and propagation on cells showed no change in glycoprotein (G gene) sequences or viral virulence compared to the ancestral virus stock. The methods developed provide valuable tools for reproducible population-level studies of IHNV epidemiology and evolution.

Multiple infection of cells changes the dynamics of basic viral evolutionary processes

The infection of cells by multiple copies of a given virus can impact viral evolution in a variety of ways, yet some of the most basic evolutionary dynamics remain underexplored. Using computational models, we investigate how infection multiplicity affects the fixation probability of mutants, the rate of mutant generation, and the timing of mutant invasion. An important insight from these models is that for neutral and disadvantageous phenotypes, rare mutants initially enjoy a fitness advantage in the presence of multiple infection of cells. This arises because multiple infection allows the rare mutant to enter more target cells and to spread faster, while it does not accelerate the spread of the resident wild-type virus. The rare mutant population can increase by entry into both uninfected and wild-type-infected cells, while the established wild-type population can initially only grow through entry into uninfected cells. Following this initial advantageous phase, the dynamics are governed by drift or negative selection, respectively, and a higher multiplicity reduces the chances that mutants fix in the population. Hence, while increased infection multiplicity promotes the presence of neutral and disadvantageous mutants in the short-term, it makes it less likely in the longer term. We show how these theoretical insights can be useful for the interpretation of experimental data on virus evolution at low and high multiplicities. The dynamics explored here provide a basis for the investigation of more complex viral evolutionary processes, including recombination, reassortment, as well as complementary/inhibitory interactions.

HIV Cell-to-Cell Spread Results in Earlier Onset of Viral Gene Expression by Multiple Infections per Cell

Cell-to-cell spread of HIV, a directed mode of viral transmission, has been observed to be more rapid than cell-free infection. However, a mechanism for earlier onset of viral gene expression in cell-to-cell spread was previously uncharacterized. Here we used time-lapse microscopy combined with automated image analysis to quantify the timing of the onset of HIV gene expression in a fluorescent reporter cell line, as well as single cell staining for infection over time in primary cells. We compared cell-to-cell spread of HIV to cell-free infection, and limited both types of transmission to a two-hour window to minimize differences due to virus transit time to the cell. The mean time to detectable onset of viral gene expression in cell-to-cell spread was accelerated by 19% in the reporter cell line and by 35% in peripheral blood mononuclear cells relative to cell-free HIV infection. Neither factors secreted by infected cells, nor contact with infected cells in the absence of transmission, detectably changed onset. We recapitulated the earlier onset by infecting with multiple cell-free viruses per cell. Surprisingly, the acceleration in onset of viral gene expression was not explained by cooperativity between infecting virions. Instead, more rapid onset was consistent with a model where the fastest expressing virus out of the infecting virus pool sets the time for infection independently of the other co-infecting viruses.

How quickly infection occurs should be an important determinant of viral fitness, but mechanisms which could accelerate the onset of viral gene expression were previously undefined. In this work we use time-lapse microscopy to quantify the timing of the HIV viral cycle and show that onset of viral gene expression can be substantially accelerated. This occurs during cell-to-cell spread of HIV, a mode of directed viral infection where multiple virions are transmitted between cells. Surprisingly, we found that neither cooperativity between infecting viruses, nor trans-acting factors from already infected cells, influence the timing of infection. Rather, we show experimentally that a more rapid onset of infection is explained by a first-past-the-post mechanism, where the fastest expressing virus out of the infecting virus pool sets the time for the onset of viral gene expression of an individual cell independently of other infections of the same cell. Fast onset of viral gene expression in cell-to-cell spread may play an important role in seeding the HIV reservoir, which rapidly makes infection irreversible.

Modeling multiple infection of cells by viruses: Challenges and insights

The multiple infection of cells with several copies of a given virus has been demonstrated in experimental systems, and has been subject to previous mathematical modeling approaches. Such models, especially those based on ordinary differential equations, can be characterized by difficulties and pitfalls. One such difficulty arises from what we refer to as multiple infection cascades. That is, such models subdivide the infected cell population into sub-populations that are carry i viruses, and each sub-population can in principle always be further infected to contain i + 1 viruses. In order to study the model with numerical simulations, the infection cascade needs to be cut artificially, and this can influence the results. This is shown here in the context of the simplest setting that involves a single, homogeneous virus population. If the viral replication rate is sufficiently fast, then most infected cells will accumulate in the last member of the infection cascade, leading to incorrect numerical results. This can be observed even with relatively long infection cascades, and in this case computational costs associated with a sufficiently long infection cascade can render this approach impractical. We subsequently examine a more complex scenario where two virus types/strains with different fitness are allowed to compete. Again, we find that the length of the infection cascade can have a crucial influence on the results. Competitive exclusion can be observed for shorter infection cascades, while coexistence can be observed for longer infection cascades. More subtly, the length of the infection cascade can influence the equilibrium level of the populations in numerical simulations. Studying the model in a parameter regime where an increase in the infection cascade length does not influence the results, we examine the effect of multiple infection on the outcome of competition. We find that multiple infection can promote coexistence of virus types if there is a degree of intracellular niche separation. If this is not the case, the only outcome is competitive exclusion, similar to equivalent models that do not take into account multiple infection of cells. We further find that multiple infection has a reduced ability to allow coexistence if virus spread is spatially restricted compared to a well-mixed system. These results provide important insights when analyzing and interpreting multiple infection models.

Mathematical models of HIV replication and pathogenesis

This review outlines how mathematical models have been helpful, and continue to be so, for obtaining insights into the in vivo dynamics of HIV infection. The review starts with a discussion of a basic mathematical model that has been frequently used to study HIV dynamics. Some crucial results are described, including the estimation of key parameters that characterize the infection, and the generation of influential theories which argued that in vivo virus evolution is a key player in HIV pathogenesis. Subsequently, more recent concepts are reviewed that have relevance for disease progression, including the multiple infection of cells and the direct cell-to-cell transmission of the virus through the formation of virological synapses. These are important mechanisms that can influence the rate at which HIV spreads through its target cell population, which is tightly linked to the rate at which the disease progresses towards AIDS.

Synaptic transmission and the susceptibility of HIV infection to anti-viral drugs

Cell-to-cell viral transmission via virological synapses has been argued to reduce susceptibility of the virus population to anti-viral drugs through multiple infection of cells, contributing to low-level viral persistence during therapy. Using a mathematical framework, we examine the role of synaptic transmission in treatment susceptibility. A key factor is the relative probability of individual virions to infect a cell during free-virus and synaptic transmission, a currently unknown quantity. If this infection probability is higher for free-virus transmission, then treatment susceptibility is lowest if one virus is transferred per synapse, and multiple infection of cells increases susceptibility. In the opposite case, treatment susceptibility is minimized for an intermediate number of virions transferred per synapse. Hence, multiple infection via synapses does not simply lower treatment susceptibility. Without further experimental investigations, one cannot conclude that synaptic transmission provides an additional mechanism for the virus to persist at low levels during anti-viral therapy.

Virus dynamics in the presence of synaptic transmission

Traditionally, virus dynamics models consider populations of infected and target cells, and a population of free virus that can infect susceptible cells. In recent years, however, it has become. clear that direct cell-to-cell transmission can also play an important role for the in vivo spread of viruses, especially retroviruses such as human T lymphotropic virus-1 (HTLV-1) and Human immunodeficiency virus (HIV). Such cell-to-cell transmission is thought to occur through the formation of virological synapses that are formed between an infected source cell and a susceptible target cell. Here we formulate and analyze a class of virus dynamics models that include such cell-cell synaptic transmission. We explore different "strategies" of the virus defined by the number of viruses passed per synapse, and determine how the choice of strategy influences the basic reproductive ratio, R0, of the virus and thus its ability to establish a persistent infection. We show that depending on specific assumptions about the viral kinetics, strategies with low or intermediate numbers of viruses transferred may correspond to the highest values of R0. We also explore the evolutionary competition of viruses of different strains, which differ by their synaptic strategy, and show that viruses characterized by synaptic strategies with the highest R0 win the evolutionary competition and exclude other, inferior, strains.